How to split command’s output and assigns result to an array using only a single expression

You can add your completer to the list of completers used by default:

zstyle ':completion:*' completer _last_command_args _complete

TL, DR:

array_of_lines=("${(@f)$(my_command)}")

First mistake (→ Q2): IFS='\n' sets IFS to the two characters \ and n. To set IFS to a newline, use IFS=$'\n'.

Second mistake: to set a variable to an array value, you need parentheses around the elements: array_of_lines=(foo bar).

This would work, except that it strips empty lines, because consecutive whitespace counts as a single separator:

IFS=$'\n' array_of_lines=($(my_command))

You can retain the empty lines except at the very end by doubling the whitespace character in IFS:

IFS=$'\n\n' array_of_lines=($(my_command))

To keep trailing empty lines as well, you'd have to add something to the command's output, because this happens in the command substitution itself, not from parsing it.

IFS=$'\n\n' array_of_lines=($(my_command; echo .)); unset 'array_of_lines[-1]'

(assuming the output of my_command doesn't end in a non-delimited line; also note that you lose the exit status of my_command)

Note that all the snippets above leave IFS with its non-default value, so they may mess up subsequent code. To keep the setting of IFS local, put the whole thing into a function where you declare IFS local (here also taking care of preserving the command's exit status):

collect_lines() {
  local IFS=$'\n\n' ret
  array_of_lines=($("$@"; ret=$?; echo .; exit $ret))
  ret=$?
  unset 'array_of_lines[-1]'
  return $ret
}
collect_lines my_command

But I recommend not to mess with IFS; instead, use the f expansion flag to split on newlines (→ Q1):

array_of_lines=("${(@f)$(my_command)}")

Or to preserve trailing empty lines:

array_of_lines=("${(@f)$(my_command; echo .)}")
unset 'array_of_lines[-1]'

The value of IFS doesn't matter there. I suspect that you used a command that splits on IFS to print $array_of_lines in your tests (→ Q3).